Evans first work in mathematical economics, entitled A Simple Theory of Competition a restatement of
Augustine Cournot's monopoly/duopoly model. Evans expanded Cournot's work significantly by exploring the analytical implications of a variety of different assumptions as to the behavior and objectives of either the monopolist or the duopolists. His following work,
The Dynamics of Monopoly, published in 1924, was one of the first to apply the
calculus of variations to economic theory. He frames the same monopolist problem now in an intertemporal framework, that is, instead of seeking immediate profit-maximization, the monopolist aims to make his profits as maximum through an interval of time. His work was followed by his Ph.D. advisee
Charles Roos who generalized his monopoly model to a case with multiple competing firms. Roos also managed to express this model within a general equilibrium framework. Roos would also be one of the three founders of the
Econometric Society alongside Norwegian economist
Ragnar Frisch and American economist
Irving Fisher. Evans participated in the foundation of the Society and became one of its first fellows. The first economist to take notice of Evans' work was
Harold Hotelling. He met personally with Evans at a meeting of the
American Mathematical Society and was immediately impressed by the scope of his work which he deemed to be a "dawning economic theory" that would bear "to the older theories the relations which the Hamiltonian dynamics and the thermodynamics of entropy bear to their predecessors". At this time, economics was not seen as a mathematical science, and many economists were even doubtful if mathematics could be useful for social sciences in general. As a result, Evans and Roos found only a small audience properly equipped to understand their works. Even so, the more mathematically inclined economists and mathematicians
E. B. Wilson,
Irving Fisher,
Henry Schultz, and
Paul Samuelson all recognized the importance of their theory. Evans main contribution to mathematical economics came in the form of his 1930
textbook Mathematical Introduction to Economics, published by
Mc Graw Hill. The book's reception, however, failed to meet Evans' expectations.
R. G. D. Allen, a colleague of Bowley, also criticized the book for not presenting a general economic theory and focusing too much on the resolution of particular problems. Some positive reviews came from Roos and Hotelling, the latter going as far as saying that the book helped "lay a groundwork upon which future contributions to political economy of first-rate importance may be expected to be based". Despite the mixed reception of his textbook, Evans continued interested in mathematical economics throughout his lifetime. In 1934 he contributed
Maximum Production Studied in a Simplified Economic System to the recently established journal
Econometrica, published on behalf of the Econometric Society. This work would later be extended by some of his students at Berkeley. He also maintained contact with the field attending seminars and presenting papers at meetings organized by the Econometric Society and the
Cowles Commission for Economic Research. During his time at Berkeley Evans arranged a weekly seminar on mathematical economics at his home. He also supervised many Ph.D. theses in the field that followed similar lines of his work. One of his most notable students was economist
Ronald Shephard, famous for his derivation of
Shephard's lemma. Shephard's 1953
Cost and Production Functions expands Evans' theoretical work on costs functions. He also restates Evans' classical dynamic monopoly problem, better incorporating expectations and price changes. His 1930 book featured two chapters where he criticized utility from the standpoint of the integrability conditions necessary to guarantee that a demand function be the result of the maximization of some utility function. ==Notable positions==